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Question:

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The temperature is high enough for formation of the thermodynamic product. Now, there are two possibilities:

Starting with the top double bond

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Or, starting from the bottom double bond,

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The answer given specifies that the second product is formed. Why is this, why isn't the first product formed?

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Both of your products have a tetrasubstituted double bond. This makes me think that they have similar stabilities, therefore there is no thermodynamically preferred product.

In both the top and bottom lines of your drawing you show the formation of allyl carbocations. You use an arrow like this "$\ce{->}$" to connect the second structure from the left to the third structure from the left. The allyl carbocation is a resonance stabilized carbocation. The second and third structures are really resonance structures and should be connected with a resonance arrow "$\ce{<->}$". Both resonance structures taken together describe the allyl carbocation.

If you compare the allyl carbocation on the top line to the one on the bottom line, you'll notice that the one on the bottom has the positive charge delocalized onto 2 tertiary carbons while the allyl carbocation on the top line has the positive charge delocalized onto 1 tertiary and 1 secondary carbon. Therefore, the bottom allyl carbocation is more stable and the product derived from it will be preferred.

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